1898 in the modern sense of "change the order of" (earlier "to change, alter, 16c. but obsolete thereafter), from Latin permutatus, past participle of permutare "change thoroughly, exchange" (see permutation). "Probably regarded by those who use it as a back-formation from permutation" [OED]. Compare permute. Related: Permutated; permutating.
late 14c., permutacioun, "interchange, concurrent change; exchange of one thing, position, condition, etc., for another," from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per "thoroughly" (see per) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). The sense of "a linear arrangement of objects resulting from a change of their order" is by 1710, originally in mathematics.
Permutation differs from combination in this, that in the latter there is no reference to the order in which the quantities are combined, whereas in the former this order is considered, and consequently the number of permutations always exceeds the number of combinations. [Century Dictionary]
early 15c., "rejected as worthless," from Late Latin reprobatus, past participle of reprobare "disapprove, reject, condemn," from Latin re- "back, again," here perhaps indicating "opposite of, reversal of previous condition" (see re-) + probare "prove to be worthy" (see probate (n.)). The meaning "abandoned in character, morally depraved, unprincipled" is by 1650s.
1900 in the biological sense, "individual or form which has arisen by or undergone (genetic) mutation," from Latin mutantem (nominative mutans) "changing," present participle of mutare "to change" (from PIE root *mei- (1) "to change, go, move"). In the science fiction sense, it is attested by 1954. As an adjective from 1903.
1878 in the physiology sense of "the sum of the chemical changes within the body by which the protoplasm is renewed, changed, or prepared for excretion," from French métabolisme, from Greek metabole "a change," from metaballein "to change," from meta "change" (see meta-) + ballein "to throw" (from PIE root *gwele- "to throw, reach"). The word also has been used in theology, poetics, and entomology.